Correct me if I am wrong. You want to access your machine running Ubuntu remotely from your mac and when you 'ssh' into your Ubuntu and when you try to 'echo $DISPLAY' you get an empty response. Probably the following solution might not work in your case, but give it a try if what you were trying is similar to what I have tried.
As you have already found one has to find the DISPLAY variable first.
So in your mac if you type as a normal user
Then what you would get is something like the following (It is the case in your hand). Anyway you all would see something similar in your systems.
Then try something like
And now you know that your display is working
Now if you want to try the same as root (Please don't jump on me guys, I know some of you all are strongly against root access), but if does not work then in your root prompt do the following
The same you found in your normal user account. Then copy your '.Xauthority' at '/Users/normal user/.Xauthority' to '/var/root/'. The .Xauthority file is already there, but this would over right it.
cp /Users/normal user/.Xauthority /var/root/
Of course the export might work, but there is no harm in doing the above. Now try the following.
And you should see the following
If you 'ssh' into Ubuntu from normal user prompt then you do not need to do the root part, but since, I use root to 'ssh' my Ubuntu systems I often have to do this.
Then when you 'ssh into Ubuntu type
And you would see something like the following
The above would work if you have done all those other bits like forwarding and etc.
Again, if you want to use root in your Ubuntu and if the 'echo $DISPLAY' does not produce any response, then try the following (Assuming you are at root prompt).
cp /home/user name/.Xauthority /root/.Xauthority
again and you would see something like the following
For fun try
And it works in my case. Hope this is helpful and would solve a problem like the one above or like mine that someone has come across and who spent a few hours on this problem while scratching head and trying to pull hair out like me :-)).